Gibbs energy minimum

G is then calculated as a linear function of (xi/xtota]) loge(xj/xtotai) and standard Simplex code was used to find the Gibbs energy minimum. 

Since the accuracy of experimental data is frequently not high, and since experimental data are hardly ever plentiful, it is important to reduce the available data with care using a suitable statistical method and using a model for the excess Gibbs energy which contains only a minimum of binary parameters. Rarely are experimental data of sufficient quality and quantity to justify more than three binary parameters and, all too often, the data justify no more than two such parameters. When data sources (5) or (6) or (7) are used alone, it is not possible to use a three- (or more)-parameter model without making additional arbitrary assumptions. For typical engineering calculations, therefore, it is desirable to use a two-parameter model such as UNIQUAC. 

The foUowiag criterion of phase equUibrium can be developed from the first and second laws of thermodynamics the equUibrium state for a closed multiphase system of constant, uniform temperature and pressure is the state for which the total Gibbs energy is a minimum, whence... 

The general criterion of chemical reaction equiUbria is the same as that for phase equiUbria, namely that the total Gibbs energy of a closed system be a minimum at constant, uniform T and P (eq. 212). If the T and P of a siagle-phase, chemically reactive system are constant, then the quantities capable of change are the mole numbers, n. The iadependentiy variable quantities are just the r reaction coordinates, and thus the equiUbrium state is characterized by the rnecessary derivative conditions (and subject to the material balance constraints of equation 235) where j = 1,11,.. ., r ... 

Furthermore, equilibria hold for ions and electrons. In every case, the Gibbs energy of the defect reaction has to provide a minimum for the equilibrium concentrations ... 

It can be shown that the maximum theoretical work produced (or minimum work required) for a process is related to the change in Gibbs energy of the process, assuming again the inputs and outputs of the process are pure components at standard conditions (Denbigh, 1956 De Nevers and Seader, 1980). 

This implies that the form of the Gibbs energy curve must pass through a minimum if defects are to be present at equilibrium (Fig. 2.1a). 

Table III gives values of the changes in Gibbs energy, enthalpy, entropy, and heat capacity of the solution process as calculated from the equations of Table I. Figure 1 shows the recommended noble gas mole fraction solubilities at unit gas partial pressure (atm) as a function of temperature. The temperature of minimum solubility is marked.

In the case of a system such as Fe-Ni, G is negative and this, combined with the ideal entropy, produces a smoothly changing curve with a single minimum (Fig. 6(a)). In this case a continuous solid solution is formed, i.e., Ni and Fe mix freely in the fc.c. lattice. However, for the case of a system such as Cu-Ag, G is quite strongly positive. In this case the addition of the ideal entropy produces a Gibbs energy curve with two minima, one at the Cu-rich end the other at the Ag-rich end (see Fig. 3.6(b) below). 

This critical position of equilibrium can be defined in two fundamentally different ways. The first is that the system A-B with composition xo has reached an equilibrium where its Gibbs energy is at a minimum. The second definition is that phases ai and Q2 with compositions x and x are in equilibrium because the chemical potentials of A and B are equal in both phases. The importance of these two definitions becomes clearer if we consider how it would be possible to write a computer programme to find x and xf. ... 

Figure 9.9. Schematic diagram of the first derivative of the G/At curve in Fig. 9.8 showing the calculation of the minimum in the Gibbs energy as a function of N. ...

According to fhe calculated minimum energy of fhe conformers, the GA was more stable than the AA conformer, but at 298.15 K the Gibbs energy of the AA conformer was 0.168 kj moU less than that of the GA conformer, indicating 52% of AA versus 48% of GA or almost equal amounts of the two conformers at equilibrium at room temperature [46]. A higher difference... 

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